I do not understand how the Inverse Laplace transform is taken of G(s).
Please see my working. I understand how the final value theorem is used, but I do not know why it is relevant to find the output, and I do not understand how the time response output is found.
I know the second line of my working is probably not right, where I take the constant A out, into it's own inverse Laplace transform. If I had
A + 1/(s+a)
then I could do it, and the two inverse laplace terms would be added together. But I am not sure how to tackle this example.